Question

If 81y^2 - k = (9y + 1/2 ) (9y - 1/2 ), then the value of k is :
2 points
a) 1/√2
b) 1/4
c) 1/2
d) none of these​

Answer 1

Answer:

the value of k is 1/4

we use the formula (a-b)( a+b) = a^2-b^2

Answer 2

$81 y^{2} - k = ( 9y + \frac{1}{2} ) ( 9y - \frac{1}{2} ) \: ( given )$

$\implies 81 y^{2} - k = (9y)^{2} - \Big(\frac{1}{2}\Big)^{2}$

/* ________________

By Algebraic Identity :

$\pink { ( a + b )( a - b ) = a^{2} - b^{2} }$

____________________*/

/* Compare bothsides, we get */

$k = \Big(\frac{1}{2}\Big)^{2}$

$\implies \red{k }\green {= \frac{1}{4}}$

Therefore.,

$Option \: \green { ( b ) } \: is \: correct$

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